Shared servers usually run linux and are actively maintained by one or more people. They use the command line to perform operations. This is the only way to ensure maximum security.
You can run a server with MAMP and access it from the internet (including the phpMyAdmin portion). But, it's not recommended because it is very insecure right out of the box. For example, the MySQL username/password is root/root by default. MAMP doesn't provide a nice interface to change these settings. (MAMP Pro does but it costs a lot of money, and only covers a few more security settings).
A truly secure system is configured using a text editor. You should know how to edit the http.conf file for Apache. MAMP's version of Apache is horrendously insecure, but is good enough for people to test web applications locally.
If you still insist on using MAMP to run a webserver, you can. You will be able to access phpMyAdmin like you usually do.
If you access MAMP's PhpMyAdmin at home from
http://localhost:8888/MAMP/frame.php?src=/phpMyAdmin/ you will have to access it as
http://255.255.255.0:8888/MAMP/frame.php?src=/phpMyAdmin/ (assuming that 255.255.255.0 is your IP address and also assuming that port forwarding is set up correctly).
You do not need to set up port forwarding if your computer is connected directly to the internet. But, if you are sitting behind a router, you do. This feature may seem like a pain sometimes, but it secures you from the outside world.
If you are interesting in continuing, Google port forwarding. See if you can get some help setting it up (it's a different process depending on what your router is). Usually routers can be configured using
http://192.168.0.1 or
http://192.168.1.1. This IP address is reserved for your internal network. If you are asked for a password, it is probably admin/blank or admin/admin or user/password or something similar.
In this interface, you can configure port forwarding. You want to take all requests for port 8888 and send it to port 8888 on your computer.
To make it more "secure", use a random port (something that's harder to guess). By default, web servers are run on port 80. So like,
http://macrumors.com:80/ will point you to the same place.